A Matlab implementation of a Mixed Numeric and Categorical attribute clustering algorithm for digital marketing segmentations. Validated via distribution analysis and segment profile. Algorithm performance characterized through convergence of intermediate variables and parameters.

1. MIXED NUMERIC AND CATEGORICAL
ATTRIBUTE CLUSTERING ALGORITHM MODELING
DR. ASOKA KORALE, C.ENG. MIET & MIESL

2. ADVANTAGES TO NUMERIC AND CATEGORICAL ATTRIBUTE CLUSTERING
Slide | 2
Improved Targeting in Campaigns & Insight in
to Segments
Currently clustering on numeric variables Age,
Net Stay, ARPU
PRIMARY ATTRIBUTES THAT CAN BE INCLUDED
WITH MIXED ATTRIBUTE TYPE CLUSTERING –
ACCOUNT TYPE, GENDER, GEO LOCATION, ……
Currently Fuzzy C – Means Algorithm used in
Clustering
Digital Advertizing SEGMENTATIONS
INCREASINGLY BASED ON CLUSTERING
Include other Categorical attributes depending
on Interest segment to create –”Micro
Segments”

3. WIDENING POTENTIAL INSIGHTS THROUGH CATEGORICAL CLUSTERING
Slide | 3
Improved
Targeting in
Campaigns &
All Attributes Can be
Clustered – leading to
very specific and
wider array of
segments
Geographic attribute clustering
to incorporate Income/ARPU
hotspots at micro level

4. CONCEPT UNDERLYING THE MIXED K PROTOTYPES ALGORITHM [1]
Slide |
4
point “d” and point “c” may switch sides
depending on how similar the numeric part and
categorical part of the point is similar to the
numeric and categorical part of the centroid
(prototype)
Influence or contribution of Numeric and
Categorical Attributes of a data point can
be controlled via a parameter “gamma”
Point “a” may switch if the categorical
part is closer to the categorical centroid
(prototype) more than its numeric part is
close to the numeric part of the centroid.
Numeric and Categorical Attributes parts
of a data point can be considered
separately and two sets of centroids act
as attractors for each Attribute type in
each cluster
Numeric Attribute1
Shapes represent two values of a single categorical variable
Numeric
Attribute2
[1]. Huang, CSIRO, Australia

5. MIXED K PROTOTYPES ALGORITHM [1]
Slide |
5
Distance measure to a prototype
(center) of two parts – numeric
and categorical
Numeric Attributes - Euclidian Distance Categorical Attributes – Dissimilarity Measure
Centroid of Numeric Attributes – a simple
average of the points in that cluster
Includes “Yij” a fuzzy membership
function if we wish to go in that
direction

6. MIXED K PROTOTYPES ALGORITHM [1]
Slide | 6
Minimize the total cost “E” which is the sum of the distances to the
numeric and categorical parts of the centroid (prototype)
Centroid of Categorical attributes
determined on highest frequency of
attribute value in each cluster

7. Slide | 7
CONVERGENCE PERFORMANCE
0 5 10 15 20 25 30 35 40
0
200
400
600
800
1000
1200
1400
1600
Total no of switches at each iteration
IterationNumber
0 5 10 15 20 25 30 35 40
1.2
1.3
1.4
1.5
1.6
1.7
1.8
x 10
4
IterationNumber
Total Distance at eachiteration
1
2
3
4
5
6
7
8
0 5 10 15 20 25 30 35 40
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
IterationNumber
Total Categorical Distance at eachiteration
1
2
3
4
5
6
7
8

8. Slide | 8
CLUSTER & SEGMENT PROFILE
1 2 3 4 5 6 7 8
0
200
400
600
800
1000
1200
Number of Cx in eachCluster
Cluster ID
20
30
40
50
60
70
80
90
1 2 3 4 5 6 7 8
Cluster/Segment ID
Age
0
50
100
150
200
250
1 2 3 4 5 6 7 8
Cluster/Segment ID
Net Stay
0
0.5
1
1.5
2
2.5
3
3.5
4
x 10
4
1 2 3 4 5 6 7 8
Cluster/Segment ID
ARPU

9. Slide | 9
VALIDATION WITH DISTRIBUTION ANALYSIS
Cluster ID
Cx in
Cluster Avg. Age
Spread
Age
Avg. Net-
Stay
Spred
Net-Stay Avg. ARPU
Spread
ARPU Post Paid Pre Paid Female Male
1 913 27 5 28 26 1231 1427 90 823 913 0
2 930 28 5 19 16 1407 1699 159 771 0 930
3 407 53 8 46 35 1095 1303 34 373 407 0
4 409 54 8 34 24 967 919 66 343 0 409
5 556 36 11 82 43 2601 2399 546 10 556 0
6 542 32 5 95 27 1031 927 0 542 67 475
7 1116 36 9 96 44 2917 2669 1116 0 0 1116
8 348 57 7 131 33 1205 853 147 201 33 315
15 20 25 30 35 40 45 50 55 60 65 70 75 80 85
0
50
100
150
200
Histogram Cx Age, Male
Age (years)
Frequency
15 20 25 30 35 40 45 50 55 60 65 70 75
0
50
100
150
Histogram Cx Age, Female
Age (years)
Frequency
Due to a certain bi-modal nature, clustering able to identify the modes in the Age histograms

10. Slide |
10
Cluster ID
Data
points in
Cluster Avg. Age
Spread
Age
Avg. Net-
Stay
Spred
Net-Stay Avg. ARPU
Spread
ARPU
Number
Post Paid
Number
Pre Paid
Number
Female
Number
Male
1 913 27 5 28 26 1231 1427 90 823 913 0
2 930 28 5 19 16 1407 1699 159 771 0 930
3 407 53 8 46 35 1095 1303 34 373 407 0
4 409 54 8 34 24 967 919 66 343 0 409
5 556 36 11 82 43 2601 2399 546 10 556 0
6 542 32 5 95 27 1031 927 0 542 67 475
7 1116 36 9 96 44 2917 2669 1116 0 0 1116
8 348 57 7 131 33 1205 853 147 201 33 315
0 12 24 36 48 60 72 84 96 108 120 132 144 156 168 180 192 204 216 228 240
0
50
100
150
200
250
Histogram Cx Network Stay
Net Stay(months)
Frequency
No identifiable structure in Net Stay distribution
VALIDATION WITH DISTRIBUTION ANALYSIS
Cluster Segment Profile

11. Slide |
11
CLUSTERING NUMERIC PART OF SEGMENTS IN 3D
-2
0
2
4
-5
0
5
-5
0
5
10
15
20
Age (normalized)
Segmental Analysis: Age, Net Stay and ARPU
Net-Stay (normalized)
ARPU(normalized)
1
2
3
4
5
6
7
8

12. Slide |
12
NOTABLE POINTS
• Allows us to cluster most attributes (within reason)
• Particularly if the categorical attributes do not have many different component
values
• Reasonable convergence performance both in terms of run time and number
of iterations
• Different dissimilarity measures and distance criteria will give differing results
• The influence of the categorical part via gamma may also need to change with
the method used
• Algorithm somewhat sensitive to initial conditions –
initialization of centroids
• Explore likelihood of falling in to a local minima and getting trapped there leading to a
sub optimal final solution
• To do…..
• Each drop can result in a non unique final result but will not impact the underlying
trends and insights in to each segment